The chairman of the club that hosts America's most prestigious golf tournament skirted the prickly issue of women's membership Wednesday, saying it is a private matter.

During his annual media session, Billy Payne, chairman of Augusta National Golf Club, did not comment specifically on Ginni Rometty, the top executive at IBM and, undoubtedly, one of the corporate world's most powerful women.

IBM's sponsorship of the Masters tournament guarantees club membership for its officers, but Rometty is a woman, and the club does not allow women to join.

"Well, as has been the case, whenever that question is asked, all issues of membership are now and have historically been subject to the private deliberation of members," Payne said. "That statement remains accurate; it remains my statement."

IBM spokesman Ed Barbini told CNN Wednesday that the company would not comment on the controversy.

The question of Rometty's membership has again brought the gender controversy to the forefront.

Now, she says, "the boys" at Augusta, members and sponsors alike, find themselves in a big bind.

"The 'woman problem' is back," she wrote in a column for CNN on Tuesday.

Burk says there are only two choices at hand: Augusta can open its doors to women, or IBM can yank its money and force its male executives to resign from the club.

"Those are the only two options that are viable that are going to wash with the public," Burk told CNN last week.

Augusta's membership -- which includes titans of industry and finance -- has been male-only since the club's opening in 1932.

When Burk tried to change things in 2002, Augusta's then-chairman, Hootie Johnson, resisted, saying that gender integration would not come "at the point of a bayonet."

In 2006, Burk was among a group of Exxon shareholders who accused the company of violating its discrimination policies by supporting the tournament.

Nonmembers can play on the course only when hosted by members.

Augusta is famously secretive about its membership, and the club declined to comment on the issue, as did IBM spokesman Chris Andrews.

"Augusta is a private club, and their personal membership is an internal matter," he said.

IBM, however, has played a role in changing policy before. The company pulled television ads from the PGA Championship when it was played at the whites-only Shoal Creek golf club in Alabama. The club admitted its first African-American in 1990 and now claims former Secretary of State Condoleezza Rice as a member.

Augusta also did not welcome its first black member until 1990, when Gannett television division president Ron Townsend joined the club.

On the eve of the 2012 Masters opening Thursday, speculation surfaced that Payne, known to be more progressive than his predecessor, will offer Rometty a membership, but only after the tournament ends and the gender debate dies down.

"Sorry, but that dog won't hunt," Burk wrote. "Telling Rometty to be a good girl and wait a little longer with IBM's collusion would be a disaster -- not only for the company's image, but for Rometty's credibility as its leader."

More and more people are asking Augusta to man up and get rid of what they say is a discriminatory policy from the past.

Payne did not announce any sweeping changes from the hot seat Wednesday. That means that Rometty will probably not show up this year in a green jacket.